Beam Load Calculator

This calculator checks a single-span beam resting on two supports, with the load spread evenly along its length: a floor joist, a lintel over an opening, a garage header or a steel beam carrying a wall. Enter the load per meter, the clear span, the material stiffness (Young's modulus, E) and the section's second moment of area (I), and it returns the peak bending moment, peak shear, midspan deflection and the span-to-deflection ratio you compare against code limits.

It does not check whether the beam is strong enough. That needs the moment compared with the section's bending capacity, plus checks for shear, bearing and lateral-torsional buckling, which depend on the material grade and design code. Use these figures to compare options and sanity-check a design, and have a structural engineer or building-control officer approve anything that holds up a building.

If your load is a point load, such as a post landing on a beam, convert it with the force calculator and see the special cases below. For joists at regular spacing, the joist span calculator works from span tables instead, and the deck calculator handles framing quantities for outdoor decks.

These are the standard Euler–Bernoulli beam results for a simply supported span, listed in every structural handbook (for example the AISC Steel Construction Manual beam diagrams and Roark's Formulas for Stress and Strain). They assume small deflections, a material that stays elastic, supports free to rotate, and a load spread evenly over the full span. They do not apply to cantilevers, continuous beams over three or more supports, or fixed-end beams, which have different coefficients.

Codes cap deflection to stop cracked finishes, bouncy floors and doors that jam. The ratio shown by the calculator is span divided by deflection, so a higher number is stiffer. Use the live-load deflection when the code limit is for live load only; this calculator uses whatever load you enter.

• Structural steel: 200–210 GPa (Eurocode 3 uses 210 GPa; US practice 29,000 ksi ≈ 200 GPa).
• Aluminum alloys: about 70 GPa, so an aluminum beam deflects roughly three times as much as the same steel shape.
• Softwood (C24, SPF, Douglas fir): roughly 9–13 GPa depending on species and grade; check the grade's mean E.
• Glulam: about 11–14 GPa depending on grade.

For steel sections, read I (the major-axis value, often Ix or Iy depending on the table's convention) from the manufacturer's or steel association's section tables. For a solid rectangle bending about its strong axis, I = b × h³ ÷ 12 with b and h in cm. Turning a joist on its side swaps b and h and cuts stiffness dramatically.

• Single point load P at midspan: M = PL ÷ 4 and δ = PL³ ÷ (48EI). A point load produces twice the moment of the same total load spread evenly.
• Cantilever with a uniform load: M = wL² ÷ 2 at the fixed end and δ = wL⁴ ÷ (8EI) at the tip, so a cantilever is far more demanding than a simple span.
• Self-weight: add the beam's own weight to w. A steel section's weight in kg/m × 0.00981 gives kN/m.
• Load from a floor area: multiply the floor load in kN/m² by the width of floor the beam supports (half the span to the next support on each side) to get kN/m.